Diff: fixed_func.cpp

Revision:

0:aa2871c4c041

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fixed_func.cpp	Wed Oct 20 02:20:46 2010 +0000
@@ -0,0 +1,133 @@
+/*
+Copyright (c) 2007, Markus Trenkwalder
+
+Portions taken from the Vicent 3D rendering library
+Copyright (c) 2004, David Blythe, Hans Martin Will
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without 
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, 
+  this list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation 
+  and/or other materials provided with the distribution.
+
+* Neither the name of the library's copyright owner nor the names of its 
+  contributors may be used to endorse or promote products derived from this 
+  software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#include "fixed_func.h"
+
+namespace fixedpoint {
+
+static const int32_t FIX16_2PI    = float2fix<16>(6.28318530717958647692f);
+static const int32_t FIX16_R2PI = float2fix<16>(1.0f/6.28318530717958647692f);
+
+static const uint16_t sin_tab[] = {
+#include "fixsintab.h"
+};
+
+int32_t fixcos16(int32_t a) 
+{
+    int32_t v;
+    /* reduce to [0,1) */
+    while (a < 0) a += FIX16_2PI;
+    a = fixmul<16>(a, FIX16_R2PI);
+    a += 0x4000;
+
+    /* now in the range [0, 0xffff], reduce to [0, 0xfff] */
+    a >>= 4;
+
+    v = (a & 0x400) ? sin_tab[0x3ff - (a & 0x3ff)] : sin_tab[a & 0x3ff];
+    v = fixmul<16>(v, 1 << 16);
+    return (a & 0x800) ? -v : v;
+}
+
+int32_t fixsin16(int32_t a)
+{
+    int32_t v;
+
+    /* reduce to [0,1) */
+    while (a < 0) a += FIX16_2PI;
+    a = fixmul<16>(a, FIX16_R2PI);
+
+    /* now in the range [0, 0xffff], reduce to [0, 0xfff] */
+    a >>= 4;
+
+    v = (a & 0x400) ? sin_tab[0x3ff - (a & 0x3ff)] : sin_tab[a & 0x3ff];
+    v = fixmul<16>(v, 1 << 16);
+    return (a & 0x800) ? -v : v;
+}
+
+int32_t fixrsqrt16(int32_t a)
+{
+    int32_t x;
+
+    static const uint16_t rsq_tab[] = { /* domain 0.5 .. 1.0-1/16 */
+        0xb504, 0xaaaa, 0xa1e8, 0x9a5f, 0x93cd, 0x8e00, 0x88d6, 0x8432,
+    };
+
+    int32_t i, exp;
+    if (a == 0) return 0x7fffffff;
+    if (a == (1<<16)) return a;
+
+    exp = detail::CountLeadingZeros(a);
+    x = rsq_tab[(a>>(28-exp))&0x7]<<1;
+
+    exp -= 16;
+    if (exp <= 0)
+        x >>= -exp>>1;
+    else
+        x <<= (exp>>1)+(exp&1);
+    if (exp&1) x = fixmul<16>(x, rsq_tab[0]);
+
+
+    /* newton-raphson */
+    /* x = x/2*(3-(a*x)*x) */
+    i = 0;
+    do {
+
+        x = fixmul<16>((x>>1),((1<<16)*3 - fixmul<16>(fixmul<16>(a,x),x)));
+    } while(++i < 3);
+
+    return x;
+}
+
+static inline int32_t fast_div16(int32_t a, int32_t b)
+{
+    if ((b >> 24) && (b >> 24) + 1) {
+        return fixmul<16>(a >> 8, fixinv<16>(b >> 8));
+    } else {
+        return fixmul<16>(a, fixinv<16>(b));
+    }
+}
+
+int32_t fixsqrt16(int32_t a) 
+{
+    int32_t s;
+    int32_t i;
+    s = (a + (1<<16)) >> 1;
+    /* 6 iterations to converge */
+    for (i = 0; i < 6; i++)
+        s = (s + fast_div16(a, s)) >> 1;
+    return s;
+}
+
+} // end namespace fixedpoint